Another interpretation of the proposed method is that we are constructing features or positional encodings for points in the manifold. Then, the approximation of the solution \(\hat{u}\)  can be seen as a non-linear combination of these features. In our case, the eigenfuctions represent feautures of increasing frequency, as seen in Figure REF . A similar concept has been proposed for cartesian domains with Fourier feature mappings [1]}, [2]}. Here, the Cartesian coordinates are transformed with sine and cosine functions, which have random frequencies that can be tuned for the problem of interest. The main difference is that in our method the frequencies are given by the eigenfunctions, and are defined in the manifold where want to solve the problem. We can select different eigenfunctions depending on the nature of problem, where high frequency problems might need a larger amount of eigenfunctions.
